Method for embedding information in sonar

The invention as disclosed is of a method to authenticate identify and trace sonar transmissions and echoes by embedding transparent, secure and robust digital watermarks in signal space, where the additional information incurs no cost in bandwidth. The complex short time Fourier transform is selected as the domain for embedding the digital watermark, secured by a secret key, in the time frequency representation of the signal. The watermark is designed through an iterative optimization step. This step insures that the watermarked sonar is also realizable. Selection of the time frequency region for watermarking is driven by avoidance of interference with the sonar itself, or in case of network operation, other watermarks. In addition, the selected time-frequency region remains robust to sound channel and other transmission effects. Sonar echoes are authenticated in the time-frequency plane by a correlation receiver tuned to the watermarked region using the secret key.